John as given you the best solutions. There is no such thing as a gel that will only affect the lab coats -- but not the faces of the people wearing them.
You must actually darken the lab coat -- or use colored ones. That's what we did for all the hospital scenes I did for years on soap operas, or even the white tops worn by the chiefs (such as Emeril) on the cooking shows, or even on a current show I light (THE DR OZ SHOW) ......in which Dr OZ wears colored scrubs and the "Assistant" is in a dyed down white coat.
DS